Google isn't always the best public DNS, depending on location and ISP another DNS may be better. If you're wanting to find the best public DNS for you I'd use Google's DNS benchmark, I can't remember the exact name but it's close to that. If you're interested just google it, I'll see if I can find a link to it. I use it everytime I move or change ISPs, granted I don't do either one of those frequently, it always seems to help my connection.

So would changing the dns on the xbox matter since it's still going through the router? Should you update dns servers on your router and keep your xbox to automatic so it chooses your router by default? I feel like such a network noob but willing to try anything that helps no matter how little..

Not always true. I have 25 download and 20 upload can't remember my ping ATM , but it's not bad. I'm living in Vegas. My friend in WV has dsl 3 dl and .5 upload. The point being I always 3 bar and he pulls host.